%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP432-1 : TPTP v9.2.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6OY96DMW8p true
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:26 PM UTC 2025
% Result : Unsatisfiable 22.09s 4.53s
% Output : Refutation 22.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP432-1 : TPTP v9.2.0. Released v2.6.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6OY96DMW8p true
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 14:20:23 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.15/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.60/0.59 % Total configuration time : 435
% 0.60/0.59 % Estimated wc time : 1092
% 0.60/0.59 % Estimated cpu time (7 cpus) : 156.0
% 0.83/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.83/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.83/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.83/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 1.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 1.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 1.22/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 22.09/4.53 % Solved by fo/fo7.sh.
% 22.09/4.53 % done 1664 iterations in 3.750s
% 22.09/4.53 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 22.09/4.53 % SZS output start Refutation
% 22.09/4.53 thf(inverse_type, type, inverse: $i > $i).
% 22.09/4.53 thf(a3_type, type, a3: $i).
% 22.09/4.53 thf(b3_type, type, b3: $i).
% 22.09/4.53 thf(multiply_type, type, multiply: $i > $i > $i).
% 22.09/4.53 thf(c3_type, type, c3: $i).
% 22.09/4.53 thf(prove_these_axioms_3, conjecture,
% 22.09/4.53 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) =
% 22.09/4.53 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) ))).
% 22.09/4.53 thf(zf_stmt_0, negated_conjecture,
% 22.09/4.53 (( multiply @ ( multiply @ a3 @ b3 ) @ c3 ) !=
% 22.09/4.53 ( multiply @ a3 @ ( multiply @ b3 @ c3 ) )),
% 22.09/4.53 inference('cnf.neg', [status(esa)], [prove_these_axioms_3])).
% 22.09/4.53 thf(zip_derived_cl1, plain,
% 22.09/4.53 (((multiply @ (multiply @ a3 @ b3) @ c3)
% 22.09/4.53 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 22.09/4.53 inference('cnf', [status(esa)], [zf_stmt_0])).
% 22.09/4.53 thf(single_axiom, axiom,
% 22.09/4.53 (( multiply @
% 22.09/4.53 A @
% 22.09/4.53 ( inverse @
% 22.09/4.53 ( multiply @
% 22.09/4.53 B @
% 22.09/4.53 ( multiply @
% 22.09/4.53 ( multiply @
% 22.09/4.53 ( multiply @ C @ ( inverse @ C ) ) @
% 22.09/4.53 ( inverse @ ( multiply @ D @ B ) ) ) @
% 22.09/4.53 A ) ) ) ) =
% 22.09/4.53 ( D ))).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl4, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X1))) @
% 22.09/4.53 (multiply @ X3 @ (inverse @ X3))) @
% 22.09/4.53 (multiply @ X0 @ X2))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl12, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (multiply @ X5 @ (inverse @ X5))) @
% 22.09/4.53 (multiply @ X0 @ X4))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X2 @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl4, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X1))) @
% 22.09/4.53 (multiply @ X3 @ (inverse @ X3))) @
% 22.09/4.53 (multiply @ X0 @ X2))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl28, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X1 @ X0)))) @
% 22.09/4.53 (multiply @ X3 @ X4))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 22.09/4.53 thf(zip_derived_cl73, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @ (inverse @ (multiply @ X0 @ (multiply @ X2 @ X4))))
% 22.09/4.53 = (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (multiply @ X2 @ (multiply @ X1 @ (inverse @ X1)))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 22.09/4.53 thf(zip_derived_cl73, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @ (inverse @ (multiply @ X0 @ (multiply @ X2 @ X4))))
% 22.09/4.53 = (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (multiply @ X2 @ (multiply @ X1 @ (inverse @ X1)))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl28])).
% 22.09/4.53 thf(zip_derived_cl651, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X3 @ (inverse @ (multiply @ X2 @ (multiply @ X1 @ X3))))
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @ (multiply @ X2 @ (multiply @ X1 @ X0)))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl73])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl4, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X1))) @
% 22.09/4.53 (multiply @ X3 @ (inverse @ X3))) @
% 22.09/4.53 (multiply @ X0 @ X2))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl12, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (multiply @ X5 @ (inverse @ X5))) @
% 22.09/4.53 (multiply @ X0 @ X4))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X2 @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl27, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X1 @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X1 @ X0)))))))
% 22.09/4.53 = (X3))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl95, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (multiply @ X1 @ X0)))
% 22.09/4.53 = (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @ (multiply @ X1 @ X0))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl27])).
% 22.09/4.53 thf(zip_derived_cl174, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ (inverse @ X0))
% 22.09/4.53 = (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1)))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl95])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl196, plain,
% 22.09/4.53 (![X0 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X5 @ (inverse @ X5)) @ (inverse @ X0))
% 22.09/4.53 = (multiply @ (multiply @ X4 @ (inverse @ X4)) @ (inverse @ X0)))),
% 22.09/4.53 inference('demod', [status(thm)], [zip_derived_cl174, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl229, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ X0) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ (inverse @ X0)))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl229])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl858, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X0 @ X1))))
% 22.09/4.53 = (inverse @ X0))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl762, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl27, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X1 @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X1 @ X0)))))))
% 22.09/4.53 = (X3))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl908, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.09/4.53 = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl27])).
% 22.09/4.53 thf(zip_derived_cl908, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.09/4.53 = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl27])).
% 22.09/4.53 thf(zip_derived_cl1059, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl908])).
% 22.09/4.53 thf(zip_derived_cl858, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X0 @ X1))))
% 22.09/4.53 = (inverse @ X0))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl762, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl12, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (multiply @ X5 @ (inverse @ X5))) @
% 22.09/4.53 (multiply @ X0 @ X4))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X2 @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl12, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (multiply @ X5 @ (inverse @ X5))) @
% 22.09/4.53 (multiply @ X0 @ X4))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X2 @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl1604, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 22.09/4.53 ((multiply @ X6 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X3 @ (inverse @ X3)) @ X0))) @
% 22.09/4.53 (multiply @ X7 @ (inverse @ X7))) @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X6))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl229])).
% 22.09/4.53 thf(zip_derived_cl1692, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1604, zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl858, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X0 @ X1))))
% 22.09/4.53 = (inverse @ X0))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl762, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl1762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))) @
% 22.09/4.53 (multiply @ X0 @ (multiply @ X2 @ (inverse @ X2))))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl907])).
% 22.09/4.53 thf(zip_derived_cl1692, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1604, zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl1811, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))) @
% 22.09/4.53 (multiply @ X0 @ (multiply @ X2 @ (inverse @ X2))))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1762, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl2327, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))) @ X0)))
% 22.09/4.53 = (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.09/4.53 (inverse @ (inverse @ X0))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1692, zip_derived_cl1811])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl0, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ X2))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('cnf', [status(esa)], [single_axiom])).
% 22.09/4.53 thf(zip_derived_cl1755, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X1 @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl908, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.09/4.53 = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl27])).
% 22.09/4.53 thf(zip_derived_cl651, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X3 @ (inverse @ (multiply @ X2 @ (multiply @ X1 @ X3))))
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @ (multiply @ X2 @ (multiply @ X1 @ X0)))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl73])).
% 22.09/4.53 thf(zip_derived_cl967, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @ (inverse @ (multiply @ X3 @ (multiply @ X2 @ X4))))
% 22.09/4.53 = (multiply @ (inverse @ X2) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X3 @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl651])).
% 22.09/4.53 thf(zip_derived_cl908, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))
% 22.09/4.53 = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl27])).
% 22.09/4.53 thf(zip_derived_cl1095, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @ (inverse @ (multiply @ X3 @ (multiply @ X2 @ X4))))
% 22.09/4.53 = (multiply @ (inverse @ X2) @
% 22.09/4.53 (inverse @ (multiply @ X3 @ (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('demod', [status(thm)], [zip_derived_cl967, zip_derived_cl908])).
% 22.09/4.53 thf(zip_derived_cl1759, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @ (inverse @ X0) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl1095])).
% 22.09/4.53 thf(zip_derived_cl2975, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (multiply @ (multiply @ X4 @ (inverse @ X4)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3))))))))
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1755, zip_derived_cl1759])).
% 22.09/4.53 thf(zip_derived_cl1755, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ X1 @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl0])).
% 22.09/4.53 thf(zip_derived_cl2990, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl2975, zip_derived_cl1755])).
% 22.09/4.53 thf(zip_derived_cl3224, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((X3)
% 22.09/4.53 = (multiply @ X3 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))) @
% 22.09/4.53 (multiply @ X2 @ (inverse @ X2))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl2327, zip_derived_cl2990])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl1692, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1604, zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl28, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X3 @ (multiply @ X2 @ (inverse @ X2))) @
% 22.09/4.53 (multiply @ X1 @ X0)))) @
% 22.09/4.53 (multiply @ X3 @ X4))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl4])).
% 22.09/4.53 thf(zip_derived_cl1708, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X4 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X5 @ (inverse @ X5))) @
% 22.09/4.53 (multiply @ X1 @ X4)))) @
% 22.09/4.53 X0)))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1692, zip_derived_cl28])).
% 22.09/4.53 thf(zip_derived_cl1692, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1604, zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl1739, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X4 @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X4)))) @
% 22.09/4.53 X0)))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1708, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl2389, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl1739])).
% 22.09/4.53 thf(zip_derived_cl762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl229])).
% 22.09/4.53 thf(zip_derived_cl2478, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (multiply @ X2 @ (inverse @ X2))))) @
% 22.09/4.53 (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl2389, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl1095, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ X4 @ (inverse @ (multiply @ X3 @ (multiply @ X2 @ X4))))
% 22.09/4.53 = (multiply @ (inverse @ X2) @
% 22.09/4.53 (inverse @ (multiply @ X3 @ (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('demod', [status(thm)], [zip_derived_cl967, zip_derived_cl908])).
% 22.09/4.53 thf(zip_derived_cl2534, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X0) @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl2478, zip_derived_cl1095])).
% 22.09/4.53 thf(zip_derived_cl1059, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl908])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl1633, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2))))
% 22.09/4.53 = (multiply @ (multiply @ X0 @ (inverse @ X0)) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl907])).
% 22.09/4.53 thf(zip_derived_cl2577, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X1 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X0) @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2))))) @
% 22.09/4.53 X1))))
% 22.09/4.53 = (X0))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl2534, zip_derived_cl1633])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl2597, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((inverse @ (multiply @ X0 @ (inverse @ X0)))
% 22.09/4.53 = (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl2577, zip_derived_cl1622])).
% 22.09/4.53 thf(zip_derived_cl1692, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X5 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X5 @ (inverse @ X5)) @
% 22.09/4.53 (inverse @ (inverse @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1604, zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl3339, plain,
% 22.09/4.53 (![X0 : $i, X3 : $i]:
% 22.09/4.53 ((X3) = (multiply @ X3 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3224, zip_derived_cl2597, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl2478, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (multiply @ X2 @ (inverse @ X2))))) @
% 22.09/4.53 (inverse @ (multiply @ (inverse @ X1) @ X0))) = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl2389, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl3435, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ (inverse @ X1)) @
% 22.09/4.53 (multiply @ X0 @ (inverse @ X0)))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3339, zip_derived_cl2478])).
% 22.09/4.53 thf(zip_derived_cl2389, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl1739])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl2990, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((X0)
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl2975, zip_derived_cl1755])).
% 22.09/4.53 thf(zip_derived_cl3653, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X1 @ (inverse @ X1)))) @
% 22.09/4.53 (multiply @ X0 @ (inverse @ X0)))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3532, zip_derived_cl2990])).
% 22.09/4.53 thf(zip_derived_cl3435, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ (inverse @ X1)) @
% 22.09/4.53 (multiply @ X0 @ (inverse @ X0)))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3339, zip_derived_cl2478])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl907, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @ (multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0))) @
% 22.09/4.53 (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl858, zip_derived_cl12])).
% 22.09/4.53 thf(zip_derived_cl762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl229])).
% 22.09/4.53 thf(zip_derived_cl1619, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X1) @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl762])).
% 22.09/4.53 thf(zip_derived_cl3771, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X3 @ (inverse @ X3)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X1) @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (inverse @ X0))))))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3717, zip_derived_cl1619])).
% 22.09/4.53 thf(zip_derived_cl3339, plain,
% 22.09/4.53 (![X0 : $i, X3 : $i]:
% 22.09/4.53 ((X3) = (multiply @ X3 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3224, zip_derived_cl2597, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl3926, plain,
% 22.09/4.53 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3771, zip_derived_cl3339, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl1059, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ X0 @ (inverse @ X0)) = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl908, zip_derived_cl908])).
% 22.09/4.53 thf(zip_derived_cl4008, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ (inverse @ (inverse @ X0))) @ X0)
% 22.09/4.53 = (multiply @ X1 @ (inverse @ X1)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3926, zip_derived_cl1059])).
% 22.09/4.53 thf(zip_derived_cl1739, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (multiply @ X4 @
% 22.09/4.53 (inverse @ (multiply @ X0 @ (multiply @ X1 @ X4)))) @
% 22.09/4.53 X0)))
% 22.09/4.53 = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl1708, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl3339, plain,
% 22.09/4.53 (![X0 : $i, X3 : $i]:
% 22.09/4.53 ((X3) = (multiply @ X3 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3224, zip_derived_cl2597, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl3736, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((X2)
% 22.09/4.53 = (multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @
% 22.09/4.53 (multiply @ X0 @ (inverse @ X0))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3717, zip_derived_cl3339])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl3898, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((X2)
% 22.09/4.53 = (multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3736, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl4359, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3898, zip_derived_cl1622])).
% 22.09/4.53 thf(zip_derived_cl3926, plain,
% 22.09/4.53 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3771, zip_derived_cl3339, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl4411, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X2)))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl4359, zip_derived_cl3926, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl762, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @ (inverse @ X2) @
% 22.09/4.53 (multiply @ (multiply @ X1 @ (inverse @ X1)) @ X0))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl229])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl3573, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X0 @
% 22.09/4.53 (inverse @ (multiply @ (inverse @ X2) @ (inverse @ (inverse @ X0)))))
% 22.09/4.53 = (X2))),
% 22.09/4.53 inference('demod', [status(thm)], [zip_derived_cl762, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl4428, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ (multiply @ X0 @ (inverse @ X1))) @
% 22.09/4.53 (inverse @ (inverse @ X0))) = (X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4411, zip_derived_cl3573])).
% 22.09/4.53 thf(zip_derived_cl5586, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ X0) @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X3 @ (inverse @ X3)))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2)))) @
% 22.09/4.53 X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1739, zip_derived_cl4428])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl3339, plain,
% 22.09/4.53 (![X0 : $i, X3 : $i]:
% 22.09/4.53 ((X3) = (multiply @ X3 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3224, zip_derived_cl2597, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl3833, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((X2)
% 22.09/4.53 = (multiply @ X2 @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3717, zip_derived_cl3339])).
% 22.09/4.53 thf(zip_derived_cl5616, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @ X0)
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2)))) @
% 22.09/4.53 X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl5586, zip_derived_cl3833])).
% 22.09/4.53 thf(zip_derived_cl6755, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((inverse @ (inverse @ (inverse @ (inverse @ X2))))
% 22.09/4.53 = (multiply @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (inverse @ (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))) @
% 22.09/4.53 X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl4008, zip_derived_cl5616])).
% 22.09/4.53 thf(zip_derived_cl3926, plain,
% 22.09/4.53 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3771, zip_derived_cl3339, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl3339, plain,
% 22.09/4.53 (![X0 : $i, X3 : $i]:
% 22.09/4.53 ((X3) = (multiply @ X3 @ (inverse @ (multiply @ X0 @ (inverse @ X0)))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3224, zip_derived_cl2597, zip_derived_cl1692])).
% 22.09/4.53 thf(zip_derived_cl3774, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((X2) = (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3717, zip_derived_cl3339])).
% 22.09/4.53 thf(zip_derived_cl6801, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X1)) @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl6755, zip_derived_cl3926, zip_derived_cl3774])).
% 22.09/4.53 thf(zip_derived_cl6845, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((X1) = (multiply @ (multiply @ X0 @ (inverse @ X0)) @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1059, zip_derived_cl6801])).
% 22.09/4.53 thf(zip_derived_cl651, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X3 @ (inverse @ (multiply @ X2 @ (multiply @ X1 @ X3))))
% 22.09/4.53 = (multiply @ X0 @
% 22.09/4.53 (inverse @ (multiply @ X2 @ (multiply @ X1 @ X0)))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl73])).
% 22.09/4.53 thf(zip_derived_cl7071, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X3 @ (inverse @ (multiply @ X2 @ (multiply @ X1 @ X3))))
% 22.09/4.53 = (inverse @
% 22.09/4.53 (multiply @ X2 @
% 22.09/4.53 (multiply @ X1 @ (multiply @ X0 @ (inverse @ X0))))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl6845, zip_derived_cl651])).
% 22.09/4.53 thf(zip_derived_cl3774, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((X2) = (multiply @ X2 @ (multiply @ X0 @ (inverse @ X0))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3717, zip_derived_cl3339])).
% 22.09/4.53 thf(zip_derived_cl7104, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i, X3 : $i]:
% 22.09/4.53 ((multiply @ X3 @ (inverse @ (multiply @ X2 @ (multiply @ X1 @ X3))))
% 22.09/4.53 = (inverse @ (multiply @ X2 @ X1)))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl7071, zip_derived_cl3774])).
% 22.09/4.53 thf(zip_derived_cl1622, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X0 @ (inverse @ X0)))) @
% 22.09/4.53 (multiply @ X1 @ X2))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl907, zip_derived_cl858])).
% 22.09/4.53 thf(zip_derived_cl4411, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @
% 22.09/4.53 (inverse @ (inverse @ (inverse @ (multiply @ X1 @ X2)))))
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl4359, zip_derived_cl3926, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl4439, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @
% 22.09/4.53 (inverse @
% 22.09/4.53 (multiply @
% 22.09/4.53 (inverse @ (inverse @ (multiply @ X2 @ (inverse @ X2)))) @
% 22.09/4.53 (multiply @ X0 @ X1))) @
% 22.09/4.53 (inverse @ (inverse @ (inverse @ (inverse @ X0))))) = (inverse @ X1))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl1622, zip_derived_cl4411])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl3717, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ X2 @ (inverse @ X2))
% 22.09/4.53 = (inverse @ (multiply @ X1 @ (inverse @ X1))))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3653, zip_derived_cl3435])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl3926, plain,
% 22.09/4.53 (![X1 : $i]: ((inverse @ (inverse @ (inverse @ (inverse @ X1)))) = (X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl3771, zip_derived_cl3339, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl4458, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @
% 22.09/4.53 (inverse @ (inverse @ (inverse @ (multiply @ X0 @ X1)))) @ X0)
% 22.09/4.53 = (inverse @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl4439, zip_derived_cl3717, zip_derived_cl3717,
% 22.09/4.53 zip_derived_cl3532, zip_derived_cl3926])).
% 22.09/4.53 thf(zip_derived_cl6801, plain,
% 22.09/4.53 (![X1 : $i, X2 : $i]:
% 22.09/4.53 ((X2) = (multiply @ (multiply @ X2 @ (inverse @ X1)) @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl6755, zip_derived_cl3926, zip_derived_cl3774])).
% 22.09/4.53 thf(zip_derived_cl3532, plain,
% 22.09/4.53 (![X0 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X2 @ (inverse @ X2)) @ X0)
% 22.09/4.53 = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl3435, zip_derived_cl2389])).
% 22.09/4.53 thf(zip_derived_cl6835, plain,
% 22.09/4.53 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl6801, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl6917, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ (multiply @ X0 @ X1)) @ X0) = (inverse @ X1))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl4458, zip_derived_cl6835])).
% 22.09/4.53 thf(zip_derived_cl8987, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (inverse @ (inverse @ (multiply @ X1 @ X0))) @ X2)
% 22.09/4.53 = (inverse @ (inverse @ (multiply @ X1 @ (multiply @ X0 @ X2)))))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl7104, zip_derived_cl6917])).
% 22.09/4.53 thf(zip_derived_cl6835, plain,
% 22.09/4.53 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl6801, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl6835, plain,
% 22.09/4.53 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 22.09/4.53 inference('sup+', [status(thm)], [zip_derived_cl6801, zip_derived_cl3532])).
% 22.09/4.53 thf(zip_derived_cl9080, plain,
% 22.09/4.53 (![X0 : $i, X1 : $i, X2 : $i]:
% 22.09/4.53 ((multiply @ (multiply @ X1 @ X0) @ X2)
% 22.09/4.53 = (multiply @ X1 @ (multiply @ X0 @ X2)))),
% 22.09/4.53 inference('demod', [status(thm)],
% 22.09/4.53 [zip_derived_cl8987, zip_derived_cl6835, zip_derived_cl6835])).
% 22.09/4.53 thf(zip_derived_cl9085, plain,
% 22.09/4.53 (((multiply @ a3 @ (multiply @ b3 @ c3))
% 22.09/4.53 != (multiply @ a3 @ (multiply @ b3 @ c3)))),
% 22.09/4.53 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl9080])).
% 22.09/4.53 thf(zip_derived_cl9086, plain, ($false),
% 22.09/4.53 inference('simplify', [status(thm)], [zip_derived_cl9085])).
% 22.09/4.53
% 22.09/4.53 % SZS output end Refutation
% 22.09/4.53
% 22.09/4.53
% 22.09/4.53 % Terminating...
% 22.46/4.68 % Runner terminated.
% 22.49/4.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------